Valence Quark Distributions in Pions: Insights from Tsallis Entropy

Abstract

We investigate the valence quark distributions of pions at a low initial scale ($Q^2_0$) by employing Tsallis entropy, a non-extensive measure that effectively captures long-range correlations among internal constituents. Utilizing the maximum entropy approach, we adopt two distinct functional forms and fit experimental data through the elegant GLR-MQ-ZRS evolution equation to derive the model parameters. Our findings indicate that the resulting valence quark distributions provide an optimal fit to experimental data, with the values of the $q$ parameter deviating from unity. This deviation indicates the significant role that correlations among valence quarks play in shaping our understanding of pion internal structure. Additionally, our computations of the first three moments of pion quark distributions at $ Q^2 = 4 \, \mathrm{GeV}^2$ display consistency with other theoretical models, thereby reinforcing the importance of incorporating valence quark correlations within this analytical framework.